> In other words, halting problem could be solved if we have sentient program which could intellectually interpret given code and say will it terminate or not

> In other words, halting problem could be solved if we have sentient program which could intellectually interpret given code and say will it terminate or not This is wrong, and the proof of the halting problem illustrates why it must be: Let's name your "sentient program" halts. That is halts(someProgram) "intellectually interprets" the code of someProgram and tells us whether running someProgram will terminate or not. Now consider the following program: def g(): if halts(g): loop_forever() What is the value of halts(g)? Either option leads to a contradiction. The article contains a few programs for which we (but also compilers nowadays) can statically determine whether they halt. This is not evidence of "intellectual interpretation solves the halting problem". It only means "there are programs for which we can determine whether they terminate", which does not in any way contradict "there cannot be a program that decides whether any arbitrary program halts eventually".